German patent document no. 196 23 334 refers to a device for determining the mass of a medium flowing in a line, having a part which is inserted into the line and in which a channel structure is provided, the channel structure including a single measuring channel in which a measuring element is situated. Devices of this kind may be used, for example, as air-mass meters in the air-intake tract of an internal combustion engine. Spray water and dust are able to enter the air-intake tract. Moreover, when shutting down the internal combustion engine, oil vapor may enter the air-intake tract through the crankshaft ventilation inlet. In the case of the familiar devices, the fluid or solid particles transported with the medium, which penetrate into the channel structure of the device, flow past the measuring element and may soil and damage it.